1. Field of the Invention
The present invention relates to a method of transferring a pattern of a reticle onto a substrate, a computer readable storage medium, and a method of manufacturing a device.
2. Description of the Related Art
In a lithography process for manufacturing a semiconductor, predetermined patterning is performed using a reticle (mask). Note, however, that when a new exposure apparatus is introduced into this process, it usually has a performance different from that of the existing exposure apparatus. For this reason, to obtain a transfer pattern identical to that obtained by the conventional exposure apparatus, the new exposure apparatus is to be adjusted.
Also, to improve the device characteristics, the current transfer pattern may be slightly modified. Ideally, in this case, it would be tempted to fabricate another reticle suited to that improvement. However, from the standpoint of practicality, it would better to form a target pattern by adjusting the exposure apparatus, instead of fabricating another expensive reticle for such a slight modification.
Exposure parameters which influence the pattern shape on a substrate (wafer) include, for example, the illumination intensity distribution, lens numerical aperture (NA), lens aberration, and light source wavelength bandwidth. Of these exposure parameters, the most influential one is the illumination condition such as the illumination mode. Although the NA is relatively influential, it has only one numeric parameter. This makes it difficult to partially adjust the NA and undesirably changes the resolving performance. Although the aberration is relatively influential as well, a leading-edge exposure apparatus has less aberration and its contribution ratio is therefore low. Under the circumstances, it is a common practice to achieve the foregoing object by adjusting the illumination condition.
There are the following two working methods of deforming a transfer pattern to have a certain target value. In the following description, the illumination mode is assumed to be generally represented by numeric parameters. For example, annular illumination is represented by the outer σ and the inner σ.
[Method 1]
First, the rate of dimensional change (to be referred to as the “sensitivity” hereinafter) in response to a change in parameter in each illumination mode is obtained for each evaluation point. Then, the amount of change from the current dimension to the target dimension at each evaluation point is divided by the sensitivity to obtain a parameter value to be changed in each illumination mode. In this case, the amount of dimensional change typically has a level on the order of several nanometers, and no large error is generated in this range even if the sensitivity is assumed to be linear. Although the sensitivity is easily obtained by optical image computation, a difference naturally occurs between an experimental value and the computed value. In view of this, a method of actually slightly changing the illumination condition and measuring the dimension experimentally is commonly employed. Details of this method are described in Proc. of SPIE, Vol. 6924, 6924Q 1-12.
[Method 2]
The contour of the pattern on the wafer is computed under a certain illumination condition. The RMS (Root Mean Square) or maximum value of a set of the differences between the values representing the computed contour and the target values at a plurality of pattern adjustment positions is obtained. The obtained value is set as an index value. Next, the illumination condition is slightly changed, and an index value is obtained for the changed illumination condition. By repeating this sequence in the space to set the illumination condition, an illumination condition under which the index value is minimum is obtained. To obtain that illumination condition, a mathematical method such as a genetic algorithm method or a Monte Carlo method is used. Details of this method are described in Shigenobu Kobayashi, “Toward A Breakthrough of Real-coded Genetic Algorithms”, Proceedings of Symposium on Evolutionary Computation 2007 (Date: Dec. 27-28, 2007; Venue: Hokkaido Toya Lake), Society for Evolutionary Computation.
The contour of the pattern on the wafer is computed by optical computation or resist image computation. Note that in this technical field, resist image computation is basically used because of the necessity of matching with the experimental results.
Resist image computation includes a scheme of physically precisely computing a resist image, and a scheme of computing a resist image based on correlation between an experimental value and the computed value of an optical image. The former scheme has the demerit of consuming a relatively long computation time, so the present invention employs the latter scheme which consumes a relatively short computation time and has features to be described later.
The computation method which uses a resist image will be explained herein. First, several types of model extraction patterns having simple line-and-space structures and line ends are selected as patterns to be transferred and measured experimentally. Although only several types of model extraction patterns are selected, they each have several tens to several hundreds of different line widths, space widths, and line end widths.
The image log slopes (ILSs) and the curvatures at feature points on these model extraction patterns are computed from their optical images.
The ILSs are defined by:ILS=d ln(I)/dx where I is the light intensity, and x is the position.
The curvatures are computed by dividing the contour into small curves, fitting them by parts of circles, and determining the radii of the circles as the curvatures. A difference δ between the computed value of an optical image and an experimental value at each of the feature points is expressed by:δ=a× curvature+b×ILS+c where a, b, and c are constants.
These values are fitted for all evaluation points to determine the constants a, b, and c. Construction of this relation is commonly called model construction. When the model is determined, the above-mentioned difference is determined by computing the ILS and the curvature from the optical image at an arbitrary position on the pattern, and the resist pattern dimension is then calculated.
In method 1, if a plurality of evaluation points are present, different illumination condition optimum solutions are sometimes obtained at these evaluation points. In this case, an averaging process or a weighting process, for example, is performed. However, such a process rarely has a physical ground, so the overall matching accuracy at all evaluation points is inevitably decreased. It is also necessary to define the contribution ratios of a plurality of existing illumination conditions. Such a process rarely has a physical ground as well, so the overall matching accuracy at all evaluation points is again inevitably lowered.
In method 2, an illumination condition under which the transfer pattern is closest to a target value is mathematically obtained. The calculated solution therefore should be theoretically correct. Despite this expectation, the practical application of the calculation result obtained in method 2 is not free from errors due to, for example, computational errors of a resist image used in a mathematical process, and deviations between the numerical definition of the illumination condition and the setting of an actual exposure apparatus.